The driving function of the Loewner equation generating slit, emanating from a zero corner | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2025. № 94. DOI: 10.17223/19988621/94/2

The driving function of the Loewner equation generating slit, emanating from a zero corner

We construct a family of mappings ƒ = ƒ (z, τ) , τ∈[0, τ0]. When τ is fixed, the mapping ƒ translates the half-plane into a strip with a cut (the length of the cut depends on the parameter τ) along the ray γ going to infinity. The cut forms zero angles with the strip boundary. The decomposition of the governing function λ(τ) of the Loewner equation at the point τ = 0, τ > 0 generating such a family of regions is obtained. We formulate a hypothesis about the behavior of the control function generating a cut emerging from the zero corner of some single-connected region along the arc of a circle. The hypothesis is tested on one particular case.

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Keywords

the Loewner differential equation, conformal mapping, the Schwarz-Christoffel integral, accessory parameters

Authors

Name	Organization	E-mail
Karmushi Maher	Tomsk State University	maherkarmoushi1996@gmail.com
Kolesnikov Ivan A.	Tomsk State University	ia.kolesnikov@mail.ru
Loboda Yulia A.	Tomsk State University	ysenchurova@yandex.ru

Всего: 3

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